Friday, February 20, 2009

Unique creations of human beings are arts and math. Great parte of human civilization has been built with the latter. With Principia Mathematica, B. Russell tried to construct a century ahead advanced math, until Wittgenstein observed that Principia statements was nothing but daughters of logic. The true is that many math systems are based on theorems proved by inferential sets of rules and axioms without additional assumptions, in which the derivation of a theorem is interpreted as evidence of truth, without further discussion, although other deductive systems achieve different interpretations. It was not surprising then that in 1931 Kurt Gödel, noted that in any formal math system was impossible to prove all truths contained in it (Incompleteness theorems : Any effectively generated theory capable of expressing elementary arithmetic can not be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but probably not in the theory). Later, Heisenberg, said that trying to improve the accuracy of the position of an object, inevitably degrades the level of certainty of the momentum.

Now David H. Wolpert(NASA Ames Research Center), argues that understanding physical universe, is beyond any intellect, because it can not be completely understood by any inferential (inductive), system. Wolpert used Cantor diagonalization to prove that any spatial sequence of events (world-lines) consistent with the laws of physics, can not be grasped by any inferential machine to predict all the conclusions of any observation or possible experiment. Equations (laws) that govern complex systems are impossible to infer. We know some laws, not all. Remember that the theory of everything is based on formal math systems. To support his theory, Wolpert established rules to measure quantities, visible phenomena, prediction of future systems or rules to remember past information with laws independent of physics, in which certain questions of the universe must necessarily be specified. Wolpert, uses mathematical entities that he called inferential devices, which operate on a set of possible universes similar to ours, where people are devices or parts of an inferential. According to Wolpert in any system of universes exist quantities that can not be determined by any inferential devices.